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We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…
We present a fast and reliable algorithm that gives precise location of breast tumours for a partial mastectomy. Our algorithm is fully implemented in the Surface Evolver, which is a general-purpose simulator of physical experiments. By…
Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell…
Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregates. We present new results of three-dimensional in vitro…
AI for cancer detection encounters the bottleneck of data scarcity, annotation difficulty, and low prevalence of early tumors. Tumor synthesis seeks to create artificial tumors in medical images, which can greatly diversify the data and…
The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during…
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
We propose a multiscale model of the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We assume that the epithelial mesenchymal-like transition between them is…
Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According…
In this paper we analyse a differential system related to a Glioblastoma growth. Using numerical simulations, we prove that model captures different kind of growth changing adequately the parameters of the model. Firstly, we make an…
In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of…
Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions…
An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot…
Rapid technological advances have allowed for molecular profiling across multiple omics domains from a single sample for clinical decision making in many diseases, especially cancer. As tumor development and progression are dynamic…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…